Question 1

A line makes an angle of 35° with the horizontal. What is the angle it makes with the vertical?

Accepted Answer

Step 1: The horizontal and vertical directions are perpendicular to each other, forming a 90° angle. Step 2: If a line makes 35° with the horizontal, it makes (90° - 35°) = 55° with the vertical. Therefore, the answer is 55°.

Question 2

Two complementary angles are in the ratio 1:5. What is the measure of the smaller angle?

Accepted Answer

Step 1: Complementary angles sum to 90°. Step 2: Let the angles be x and 5x. Step 3: x + 5x = 90°. Step 4: 6x = 90°, so x = 15°. Step 5: The smaller angle = 15°. Therefore, the answer is 15°.

Question 3

Three lines meet at a point. The angles formed are in the ratio 2:3:4. What is the measure of the largest angle?

Accepted Answer

Step 1: When three lines meet at a point, the sum of all angles around that point is 360°. Step 2: Let the angles be 2x, 3x, and 4x. Step 3: 2x + 3x + 4x = 360°. Step 4: 9x = 360°, so x = 40°. Step 5: The largest angle = 4x = 4(40°) = 160°. Therefore, the answer is 160°.

Question 4

A transversal intersects two parallel lines. If one of the alternate interior angles is 72°, what is the measure of the other alternate interior angle?

Accepted Answer

Step 1: When a transversal cuts two parallel lines, alternate interior angles are equal. Step 2: If one alternate interior angle is 72°, the other alternate interior angle is also 72°. Therefore, the answer is 72°.

Question 5

Two lines intersect and form four angles. If one of the angles is 65°, what is the measure of the angle adjacent to it?

Accepted Answer

Step 1: When two lines intersect, adjacent angles are supplementary (they add up to 180°). Step 2: If one angle is 65°, then the adjacent angle = 180° - 65° = 115°. Therefore, the answer is 115°.

Question 6

Two supplementary angles are in the ratio 3:7. What is the measure of the larger angle?

Accepted Answer

Step 1: Supplementary angles sum to 180°. Step 2: Let the angles be 3x and 7x. Step 3: 3x + 7x = 180°. Step 4: 10x = 180°, so x = 18°. Step 5: The larger angle = 7x = 7(18°) = 126°. Therefore, the answer is 126°.

Question 7

A transversal cuts two parallel lines. If one of the co-interior angles is 108°, what is the other co-interior angle?

Accepted Answer

Step 1: Co-interior angles (also called consecutive interior angles or same-side interior angles) are supplementary when a transversal cuts parallel lines. Step 2: They sum to 180°. Step 3: If one angle is 108°, the other = 180° − 108° = 72°.

Question 8

Three lines meet at a point. If the angles formed are in the ratio 1:2:3, what is the measure of the smallest angle?

Accepted Answer

Step 1: Three lines meeting at a point form angles that sum to 360°. Step 2: Let the angles be k, 2k, and 3k. Step 3: k + 2k + 3k = 360°. Step 4: 6k = 360°. Step 5: k = 60°. Step 6: The smallest angle = k = 60°.

Question 9

Two adjacent angles on a straight line are in the ratio 2:7. What is the measure of the larger angle?

Accepted Answer

Step 1: Adjacent angles on a straight line are supplementary (sum to 180°). Step 2: Let the angles be 2k and 7k. Step 3: 2k + 7k = 180°. Step 4: 9k = 180°. Step 5: k = 20°. Step 6: The larger angle = 7k = 7 × 20° = 140°.

Question 10

Two lines intersect such that one of the angles formed is 65°. If a third line is drawn parallel to one of the original lines, what is the angle between the third line and the second original line (corresponding angle)?

Accepted Answer

Step 1: When two lines intersect, one angle is 65°. Step 2: The vertically opposite angle is also 65°, and adjacent angles are 180° − 65° = 115°. Step 3: When a third line is drawn parallel to one of the original lines, corresponding angles are equal. Step 4: The angle between the third line and the second original line equals the angle between the first and second original lines. Step 5: Since one angle of intersection is 65°, the corresponding angle formed by the parallel line is also 65°.

Question 11

Two lines intersect forming four angles. If one angle is 4 times another angle, what is the measure of the larger angle?

Accepted Answer

Step 1: When two lines intersect, adjacent angles are supplementary (sum to 180°). Step 2: Let the smaller angle be x. Then the larger adjacent angle is 4x. Step 3: x + 4x = 180°. Step 4: 5x = 180°. Step 5: x = 36°. Step 6: The larger angle = 4x = 4 × 36° = 144°.

Question 12

Two parallel lines are cut by a transversal. One of the co-interior angles (also called consecutive interior angles) is 35° more than the other. What is the measure of the larger co-interior angle?

Accepted Answer

Step 1: Co-interior angles are supplementary, meaning they sum to 180°. Step 2: Let the smaller angle be x°. Then the larger angle is (x + 35)°. Step 3: x + (x + 35) = 180°, so 2x + 35 = 180°, giving 2x = 145°, thus x = 72.5°. Step 4: The larger angle = 72.5° + 35° = 107.5°.

Question 13

In a quadrilateral ABCD, angles A, B, C are in the ratio 1:2:3 respectively. If the exterior angle at D is 72°, what is angle A?

Accepted Answer

Step 1: The exterior angle at D is 72°, so the interior angle D = 180° − 72° = 108°. Step 2: The sum of interior angles in a quadrilateral = 360°. Step 3: Let angles A, B, C be x, 2x, 3x respectively. Then x + 2x + 3x + 108° = 360°. Step 4: 6x + 108° = 360°, so 6x = 252°, giving x = 42°. Step 5: Angle A = 42°.

Question 14

In a triangle ABC, the exterior angle at vertex B is 125°. If the interior angle at A is 48°, what is the exterior angle at vertex C?

Accepted Answer

Step 1: The exterior angle at B is 125°, so the interior angle at B = 180° − 125° = 55°. Step 2: In triangle ABC, the sum of interior angles = 180°. So angle A + angle B + angle C = 180°. Step 3: 48° + 55° + angle C = 180°, giving angle C = 77°. Step 4: The exterior angle at C = 180° − 77° = 103°.

Question 15

Three lines meet at a point. The angles between consecutive pairs of lines are in the ratio 2:3:4. If one of these angles is 80°, which of the following could be the sum of the two smallest angles?

Accepted Answer

Step 1: Let the three angles be 2x, 3x, and 4x. Step 2: These three angles around a point sum to 360°: 2x + 3x + 4x = 360°, so 9x = 360°, giving x = 40°. Step 3: The three angles are 80°, 120°, and 160°. Step 4: The two smallest angles are 80° and 120°, so their sum = 200°.

Question 16

Two straight lines intersect such that one of the angles formed is 35°. A third line is drawn parallel to one of the original lines. If this third line intersects the second original line, what is the angle between the third line and the second original line (taking the acute angle)?

Accepted Answer

Step 1: When two lines intersect, they form angles of 35° and 145° (supplementary). Step 2: When a line parallel to the first original line intersects the second original line, by the property of corresponding angles (or alternate angles), the angle formed equals one of the angles at the original intersection. Step 3: The acute angle between the third line and the second original line will be either 35° or 145°. Since we need the acute angle, the answer is 35°.

Question 17

Two intersecting lines form four angles. If one angle is 4 times another angle, what is the measure of the smallest angle formed?

Accepted Answer

Step 1: When two lines intersect, they form two pairs of vertically opposite angles. Adjacent angles are supplementary. Step 2: Let the smallest angle be x°. Then the adjacent angle is (180 − x)°. Step 3: According to the problem, one angle is 4 times another. If x is the smallest, then either 180 − x = 4x or the vertically opposite angle relationship applies. Step 4: If 180 − x = 4x, then 180 = 5x, so x = 36°. Step 5: The four angles are 36°, 144°, 36°, 144°. The smallest is 36°.

SSC CPO Angles & Lines

SSC CPO Angles & Lines — Past Exam Questions

Angles & Lines— Rules & Concept

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60-Second Revision — Angles & Lines